BAGHDAD, Iraq (CNN) -- A man claiming to be the leader of al Qaeda in Iraq mocked the death toll of American troops and urged his fighters to launch an offensive against U.S. forces in the next few weeks.

Abu Hamza al-Muhajir, also known as Abu Ayyub al-Masri, is the leader of al Qaeda in Iraq.

The speaker was identified as Abu Hamza al-Muhajir, also known as Abu Ayyub al-Masri, on several Islamist Web sites that posted the recording.

"The reason I give this speech is that the enemy declared -- even though it might be lying -- that its death toll in Iraq has reached 4,000," he said.

"So we call upon our heroes ... to ask every group within a month from the time it hears this, to offer the head of an American as a gift to the deceitful [President] Bush," he continued.

As of Saturday, 4,036 U.S. troops had died in the Iraq war.

The speaker also called for attacks on members of Iraqi awakening councils, a movement of predominantly Sunnis who have joined forces with the U.S. and Iraqi governments in battling Islamic jihadists loyal to al Qaeda in Iraq.

Also Saturday, radical Shiite cleric Muqtada al-Sadr threatened to "declare a war" unless U.S. and Iraqi forces stop their assaults on his followers.

"I'm giving the last warning and words to the Iraqi government," al-Sadr said in a statement on a loyalist's Web site.

"They should take the road of peace and drop the violence that they use with their people. Otherwise, they will be like the destructive [Saddam Hussein] government."

The cleric also assailed the United States, saying, "From the other side, the occupier made us targets for his planes, tanks, mortars and his deceptive policy by demanding me not to stand against the Iraqi government, which -- if it weren't for us -- it would not exist.

"It is like the occupier would ignore the fact that his army is standing against the government, to prevent it from being an independent government with full sovereignty."

The warning was a reminder of al-Sadr's bloody rebellions in 2004 against U.S. forces in Najaf and Baghdad.

Al-Sadr recently renewed for six months the cease-fire he imposed in August on his Mehdi Army militia, a move that the U.S. military has credited with helping reduce violence across Iraq.

But an uprising like the one al-Sadr threatened Saturday would ultimately fuel inter-Shiite fighting through Sadr City and other Shiite communities.

Intense fighting between Iraqi security forces and al-Sadr's Mehdi Army continued Saturday in the southern city of Nasiriya and in Sadr City, the cleric's Baghdad stronghold.

Twelve people were killed in overnight fighting Friday into Saturday between Iraqi security forces and the Mehdi Army in Sadr City, an Interior Ministry official said. Six dozen people were wounded.

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In Nasiriya, sporadic clashes spilled into Saturday, leaving four police officers and 16 militia members dead, the ministry official confirmed. The clashes prompted authorities to impose a curfew in the city Saturday.

In another southern city, Diwanyia, which witnessed deadly fighting between Iraqi forces and the Mehdi Army last month, officials discovered 14 decapitated bodies. An interior ministry official said the bodies appear to be a few days old.

Meanwhile, Iraqi troops began a new phase of the security operation launched March 25 by Prime Minister Nuri al-Maliki, dubbed Charge of the Knights. The operation aims to clear militants from their strongholds in the southern Iraqi city of Basra, a spokesman for the British army said.

The operation began early Saturday in the Hayania district, with British artillery and U.S. aircraft hitting open ground as a show of force, Maj. Tom Holloway said.

Iraqi troops, working with U.S. and British military teams, were in control of Hayania by the afternoon, said Maj. Gen. Abdul Karim Khalaf, a spokesman for the Iraqi Interior Ministry.

The troops did not face much resistance but encountered explosives planted on the roads as they entered, Khalaf said. They were able to defuse them and were searching house to house for wanted "criminals" and illegal weapons.

"As with the earlier phases ... this continues to be an Iraqi-led, -planned and -executed mission," Holloway said. "Coalition troops are ready to provide support to Iraqi Security Forces as requested and required."

Al-Sadr's warning -Saturday came after he agreed to al-Maliki's order to vacate and turn over his headquarters in Basra to Iraqi Security Forces.

On Friday, they surrounded the office and gave workers until the end of Saturday to leave what they said was government property.

Al-Sadr's comments also wrap up a week of violence illustrating the ever-sharpening divide among Iraq's majority Shiites: those who back al-Sadr and those who support al-Maliki and the Supreme Islamic Council of Iraq.

The council is the main Shiite group in al-Maliki's U.S.-supported government.E-mail to a friend